1. Field of the Invention
The present invention relates to symbol timing recovery in a receiver of a digital communications system.
2. Description of the Related Art
In many digital communications systems, a user generates digital information that is then processed into an encoded (e.g., error-correction encoded) and/or packetized stream of data. The stream of data is then divided into discrete blocks. Each of the blocks is mapped onto a corresponding one of a sequence of code or symbol values (“symbols”) chosen from a pre-defined alphabet A, and generated with a period Ts, sometimes referred to as the “baud” rate. Symbols may then be used to modulate an analog, e.g., radio frequency (RF) carrier, in amplitude, phase, and/or frequency prior to physical transmission through the communication medium. Many methods of mapping exist and are well known in the art, and these pre-defined alphabets are generated based on certain criteria. For example, data may be mapped into symbols of a complex data stream as pairs of in-phase (I) and quadrature phase (Q) component values. I and Q component values of the complex data stream may then be used to modulate cosine and sine components of a quadrature oscillator that are subsequently upconverted to an RF carrier. Modulation formats such as quadrature amplitude modulation (QAM) and vestigial sideband amplitude modulation (VSB) are common formats used for transmission of digital television signals in accordance with, for example, the ATSC standard for digital television, “ATSC Digital Television Standard,” Doc. A/53, September 1995.
The modulated carrier signal transmitted through the medium (e.g., wire, optical fiber, atmosphere, space, magnetic recording head/tape, etc.) comprises a series of analog pulses, each analog pulse being amplitude or phase modulated by a corresponding symbol in the sequence. The pulse shape used typically extends many symbol periods in time. This introduces the possibility of adjacent pulses corrupting each other, a phenomenon known as inter-symbol interference (ISI).
As is known in the art, transmit and receive filters may be selected to minimize the effects of ISI. A pulse shape is selected so as to provide i) a high amplitude signal at or near the sampling instant, ii) a rapid rate of decay past the sampling instant, iii) a zero-value at integer multiples of the baud rate, and iv) a realizable (or very closely approximate) implementation. Thus, the pulse shape is selected such that it obeys the well known “Nyquist pulse shaping criterion for zero ISI” as stated in condition (iii). As is known in the art, transmit and receive filters are usually selected so that when they are in cascade in the signal path a desired pulse shape is produced for a detector. For example, a commonly used filter that provides a “Nyquist pulse” may have its impulse response selected from the raised cosine family of functions. The transmit and receive filters are then selected as root-raised cosine filters. FIG. 1A shows a sequence of three raised cosine (Nyquist) pulses 101, 102, and 103, the first two instances corresponding to a bit value and the third instance corresponding to a complement bit value. The symbol repetition period, Ts, is the time between the largest, unity-valued peaks of two consecutive pulses in the sequence.
FIG. 1A shows three consecutive instances of a raised cosine pulse with ideal sampling (sampling period equals the symbol repetition period Ts and phase τ=0). In FIG. 1A, when the pulse is sampled at top-center of the unity-valued peaks, the amplitude measured at time equal 30 (arbitrary time base), is the sum of amplitudes of the three pulses, or a+b+c. Note that the contribution from adjacent pulses is zero (because b=c=0), so no ISI effect is introduced. In general, with ideal sampling, the signal contribution of other pulses is zero at non-zero, integer multiples of the symbol repetition period Ts. Ideal sampling of the sequence of pulses, therefore, results in zero ISI.
FIG. 1B shows these same three consecutive instances of a raised cosine pulse with one form of non-ideal sampling (e.g., sampling with period equal to symbol period Ts and sampling phase τ≠0). In FIG. 1B, when the pulse is sampled at time equal 28, the amplitude measured is again the sum of amplitudes of the three pulses, or a+b+c. However, unlike the sampling of FIG. 1A, the signal contribution of the other pulses, b and c, is now non-zero even though the sampling period is still Ts. This illustrates how non-ideal sampling introduces ISI effects.
Thus, it is desirable for a receiver to sample a received signal of consecutive pulses at nearly ideal sampling instances. When nearly ideal sampling is achieved, the signal is said to be sampled at “top dead center” of the symbol period, which also represents the “ideal sampling phase.” Many factors combine to make this task difficult for a receiver, including the unknown propagation delay from the transmitter to the receiver, possible mismatch in the oscillator frequencies in the transmitter and receiver (causing the relative delay to drift over time), and multipath signal interference. For these reasons, a receiver both estimates and tracks the relative timing offset, which is referred to in the art as “timing recovery” and/or “symbol/baud synchronization.”
A receiver performs several functions to demodulate and decode a received signal. Receiver functions include, for example, tuning and RF demodulation of the received signal to an intermediate frequency (IF) signal; synchronization of the carrier loop to the RF carrier; symbol timing recovery (baud synchronization); sampling according to the baud rate or symbol period; equalization; symbol detection; and decoding. After RF demodulation, the received signal is sampled by, for example, an analog-to-digital (A/D) converter. Timing recovery attempts to both detect the symbol repetition period Ts and synchronize sampling instances to the top-dead-center of the pulse shapes. The timing recovery system then tracks variations in the detected period of Ts. A subsequent detector examines each sample to generate either a soft or hard decision for the symbol that corresponds to the sample. The present invention is concerned with the timing recovery function of the receiver.
Many methods exist in the art for timing recovery. One method uses a separate pilot tone in phase with the modulation process that is transmitted in addition to the information-bearing signal. The receiver derives the symbol timing information from the pilot tone. However, including a reference timing signal reduces channel throughput (and uses both extra power and bandwidth) for pilot tone transmission and reception. Consequently, many applications use blind techniques for symbol timing, and also equalization.
With blind techniques, timing information is derived directly from the received signal itself. An “error tracking synchronizer” continually estimates and tracks the timing error present, and adjusts a locally generated timing reference responsive to the error estimate. A “feedforward synchronizer” does not continually adjust a locally generated reference based on an error estimate, but instead processes the received signal to directly generate the reference. Feedforward synchronizers are often employed in burst-mode communication systems. In either error tracking or feedforward synchronizers, a “decision directed” synchronizer utilizes the receiver's estimates of the transmitted symbol values to synthesize the timing estimate. The synchronizer is termed a “non-data-aided” synchronizer, since no data is transmitted without user content to aid in timing recovery.
Synchronizers may operate in continuous time, discrete time, or a combination of both continuous and discrete time. Continuous time synchronizers apply the reference signal generated by the synchronizer to the clock of the A/D converter, thereby adjusting the actual sampling period of the analog input signal. Conversely, discrete time synchronizers leave the A/D converter in a “free-running” mode and apply the timing reference to a digital interpolator that adjusts the phase of the digital sample sequence.
FIG. 2 shows a block diagram of a prior art timing recovery system 200 that may be employed in a receiver. Timing recovery system 200 receives sample sequence y[n] from A/D converter 201 coupled to demodulator 222. A/D converter 201 is in “free-running” mode and is governed by a free running oscillator 202. The sample sequence y[n] is not synchronized to the symbol phase τs or period Ts. Timing recovery module 200 includes digital interpolator 203 that adjusts the phase τ and period T of the digital sample sequence to generate y[nT+τ] (also labeled herein as yn(τ)). Interpolator 203 may be implemented with a poly-phase filter. The interpolated sequence yn(τ) is in relatively close synchronization with the symbol period Ts and phase Ts.
The interpolated sequence yn(τ) is passed to timing phase detector 204. Timing phase detector 204 generates an estimate of the timing phase error (termed herein as “phase error” eτ) that represents the difference between the actual sampling phase τ and the ideal sampling phase τs. The phase error eτ is then filtered with loop filter 205 to reject high frequency components of the signal and integrate phase over time to adjust frequency. Local timing reference 206, shown in FIG. 3 as a numerically controlled counter (NCC), uses the filtered version of error estimate eτ from loop filter 205 to adjust phase and/or period of the timing reference signal used to drive sampling of the signal. The reference of local timing reference 206 controls interpolator 203 in a way that tends to drive the phase error eτ toward a fixed mean point, typically set as zero.
An alternative embodiment for a prior art timing recovery system 300 is shown in FIG. 3, in which the phase error eτ is used to adjust the sampling clock on A/D converter 301 directly. The sampled sequence yn(τ) is passed through timing phase detector 204 which generates an estimate of phase error eτ in a manner similar to that of FIG. 2. The phase error eτ is filtered with loop filter 205 and provided to local timing reference 306. Local timing reference 306, shown in FIG. 3 as voltage controlled oscillator (VCO), uses the filtered phase error eτ from loop filter 205 to adjust phase and/or period of its output reference signal. The reference signal of local timing reference 306, in turn, controls A/D converter 301 in a way that tends to drive the phase error eτ toward a fixed mean point, typically set as zero.
Many methods exist in the prior art that may be employed by timing phase detector 204 to calculate the error estimate eτ from the sequence yn(τ). One such technique defines a cost criterion (also referred to as a cost function) that is a function of the timing phase τ. Timing phase τ is adjusted to a value that minimizes the cost function by a gradient descent technique. The value of τ which minimizes the cost function also causes the derivative of the cost function with respect to τ (also known as the “gradient function”) to be zero. Thus, the desired timing phase may be found by adjusting, or stepping, the value of τ in a direction opposite to the sign of the cost function (i.e., mathematically, the trajectory of the parameter τ descends the steepest slope of the cost function). Therefore, this approach is sometimes termed a gradient descent strategy.
These prior art methods generally calculate the gradient of a mean squared error (MSE) function. The MSE cost function JMSE is defined as the expected value of the square of the difference between a received digital sample yn(τ) and the actual transmitted symbol s as in equation (1):JMSE=E[|yn(τ)−s|2]  (1)where E[●] denotes the mathematical expectation, or “expected value of” “●.”
The derivative of JMSE with respect to τ, dJMSE/dτ, may be used as the phase error eτ, and may be written as in equation (2):dJMSE/dτ=(dJMSE /dyn (τ))dyn(τ)/dτ  (2)where the first term on the right-hand side, (dJMSE/dyn (τ)), is the derivative of JMSE with respect to yn (τ), which is proportional to |yn(τ)−s|. For typical implementations, the expectation operator is omitted and instantaneous values are used by the process instead. The derivative dJMSE/dyn (τ) is the least mean square (LMS) error term and is defined as eLMS[n] in the timing phase detector error of equation (2′):dJMSE/dτ=eLMS[n] dyn(τ)/dτ.  (2′)where eLMS[n]=|yn(τ)−s|. Computation of dyn (τ)/dτ may be approximated using a finite impulse response (FIR) filter, such as described in Lee and Messerschmitt, Digital Communication, Appendix 17-B, Kluwer Academic Publishers, Norwell, Mass., Second Edition, 1994, which is incorporated herein by reference.
The error term eLMS[n] depends on the transmitted symbol value s. Actual symbol values may be available as an acquisition aid to the receiver during a training period. However, if either no training interval is defined in the system or the training period is insufficient for reliable acquisition, the receiver may use its estimates of the transmitted symbols instead (referred to as “decision directed” mode). These decision-directed systems are examples of blind signal systems, since they process a received signal without knowledge of the actual transmit symbol information. Under these conditions, before adequate convergence of the timing loop, the estimates of the transmitted symbols are prone to error, making decision directed adaptation unreliable. When the system has stabilized using some other acquisition method, the receiver then switches to the decision-directed gradient method for tracking.
Many blind techniques exist for timing recovery based on the demodulated signal. For example, some systems may use a timing phase detector which obtains a timing estimate from both high-pass and low-pass filtered versions of the demodulated signal. Such a system is disclosed in U.S. Pat. No. 5,872,815 to Strolle et al., entitled “Apparatus for Generating Timing Signals for a Digital Receiver,” which is incorporated herein by reference.
A receiver also generally applies equalization to the sample sequence prior to forming hard decisions for symbols from the received sample sequence. Equalization is used to reduce the effects of ISI, caused by phenomena such as i) residual timing error (for example as in FIG. 1B), ii) multipath distortions from the propagation channel, and/or iii) approximations to the ideal transmit and receive filters for ease of implementation. As with timing recovery, the samples representing the received symbols are filtered by equalizer coefficients, which are adjusted to minimize a cost function.
One such blind cost criterion employed for equalization is the constant modulus (CM) criterion. The stochastic gradient descent of the CM criterion for equalization is known as the Constant Modulus Algorithm (CMA). The CMA algorithm is described in an article by D. N. Godard entitled “Self-Recovering Equalization in Two-Dimensional Data Communication Systems,” IEEE Transactions on Communications, vol. 28, no. 11, pp. 1867–1875, October 1980, which is incorporated herein by reference. The CM criterion and CMA algorithm were further developed to de-couple equalization and carrier recovery functions in a receiver. Such use of CM criterion and CMA algorithm for equalization is described in J. R. Treichler et al., “A New Approach to Multipath Correction of Constant Modulus Signals,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-31, no. 2, April 1993, which is incorporated herein by reference. Systems that use such CMA algorithm for adaptive equalization, such as that described in U.S. Pat. No. 5,872,815 to Strolle et al., do not employ the CM criterion or its variants for timing recovery.